The clinical stakes are considerable. The aorta is the body’s largest blood vessel, the highway that carries oxygen-rich blood from the heart to every organ and limb. When this vessel is pinched or narrowed as it exits the heart, a hallmark of coarctation of the aorta, blood flow to the lower body is restricted and the fetal heart must pump harder to push blood through the constriction. The condition accounts for an estimated 6% to 8% of all cardiac birth defects, making it one of the more frequently encountered diagnoses a fetal cardiologist must consider. Yet despite its prevalence, coarctation remains one of the most challenging defects to identify prenatally.

The reason for that difficulty lies in the limitations of current screening tools. Standard prenatal testing relies primarily on anatomic information, essentially static pictures of the heart’s structure, rather than on dynamic blood-flow data, to assess fetal heart health. Standard ultrasound and even specialized echocardiograms, noninvasive tests that use sound waves to create images and generate data about a fetus, often fail to detect anatomical and blood flow abnormalities in a developing heart. Worse, ultrasound-based tests sometimes produce false positives, suggesting that an abnormality is present when no such defect actually exists. “Standard prenatal testing and even specialized imaging often fail to detect anatomical problems in the fetal aorta,” Wei says. “By integrating detailed blood flow parameters, we will give doctors a more precise tool to use when diagnosing congenital heart defects.”

The consequences of a missed diagnosis can follow a child for a lifetime. If coarctation of the aorta is not diagnosed early and repaired with surgery, infants can suffer long-term health problems such as high blood pressure, or in severe cases, die. Early detection changes the entire trajectory of care. When clinicians and families know before birth that a defect is present, they can plan for delivery at a center equipped for immediate intervention, schedule surgical repair, and monitor the newborn closely from the first hours of life. “Surgeons can repair many heart problems in babies, but the first, and most important, step is detecting problems,” Wei said. “The earlier we can identify a condition, the more time clinicians and families have to plan for the baby’s care.”

Wei’s answer to this diagnostic gap is a digital twin: a viewable digital replica of an individual patient’s cardiovascular system that can be interrogated on a computer the way a clinician might examine a patient at the bedside. The model will integrate multidimensional, patient-specific data to support clinical decision-making, including assessment of whether a fetal heart defect is present. Rather than relying on a single snapshot of anatomy, the digital twin will simulate how blood actually behaves inside a particular fetus’s aorta, capturing the hemodynamic signatures that a narrowing leaves on pressure, velocity, and wall stress even when the structural change is too subtle for imaging to resolve.

The raw material for this model comes from an unusually rich data source. Wei’s team will draw on fetal heart data collected at more than 15 cardiology programs across North America that are part of the Fetal Heart Society. The database includes information gathered during two-dimensional and three-dimensional ultrasound tests performed on hundreds of racially and ethnically diverse pregnant women, including some whose babies were confirmed after birth to have heart defects. That breadth matters both scientifically and clinically: a model trained on diverse populations is more likely to perform reliably across the full spectrum of patients a prenatal clinic will see, and the inclusion of confirmed postnatal diagnoses gives the researchers ground truth against which their predictions can be checked.

Wei and his team have already used information in the database to create a model representing blood flow in healthy fetal hearts, establishing a baseline of normal hemodynamics. Going forward, the new model will focus on a set of physically meaningful measurements that reflect how the cardiovascular system responds to obstruction. These include the forces exerted on the walls of fetal blood vessels, the pressure and flow characteristics through a narrowed fetal artery, and the resistance that arises when freshly pumped blood collides with blood already moving through the vessel. Each of these parameters encodes information about the geometry and elasticity of the aorta in ways that a static image cannot, which is precisely why the researchers believe flow-based metrics will outperform anatomy-only assessment.

Building a model is only half the challenge; proving that it is trustworthy is the other half. To validate their computational predictions, the researchers will conduct laboratory experiments using 3D-printed silicone models of fetal aortas, paired with fluid and pumping mechanisms that recreate the mechanical conditions of the fetal circulation. These physical phantoms allow the team to compare what the digital twin predicts against what actually happens in a controlled, measurable system with known geometry. Finally, data from the Geisinger healthcare system’s database will be used to evaluate blood flow metrics for better diagnosis of aorta narrowing in the future, closing the loop between computation, experiment, and real clinical outcomes.

The project is a deliberately interdisciplinary effort. Wei is working with Professor Zhongqiang Zhang and Associate Professor Fangfang Wang, both of WPI’s Department of Mathematical Sciences, whose expertise in computational mathematics underpins the numerical machinery of the digital twin, and with Dr. Shuping Ge, a pediatric cardiologist and researcher with the Geisinger healthcare system in Pennsylvania, who brings the clinical perspective needed to ensure the model answers questions doctors actually face. The work also builds on Wei’s broader research program in computational and experimental models of blood flow mechanics. His fetus-related research has been supported by the American Heart Association’s Second Century Faculty Independence Award and a National Institute of Biomedical Imaging and Bioengineering Trailblazer Award, honors recognizing the innovation and potential clinical impact of his work, and he has previously collaborated on pediatric medical devices and 3D-printed blood vessels for heart bypass surgery.

For Wei, the ultimate measure of success is not a publication or a patent but a change in how early and how confidently fetal heart defects are caught. He says that development of a validated digital twin model for coarctation of the fetal aorta will lay a solid foundation for future human studies that could lead to more accurate screening tools and better health outcomes for children with the birth defect. “The goal of my lab is to improve the detection and treatment of cardiovascular disease and, ultimately, to help ensure that patients receive the right care at the right time,” Wei said. If the project succeeds, the faint hemodynamic whispers of a narrowed aorta, invisible to today’s ultrasound screens, may become impossible for medicine to miss.

Subject of Research: Development of a blood flow-based digital twin model for prenatal detection of fetal aortic coarctation

Article Title: Worcester Polytechnic Institute researcher is seeking clues to problems in tiny hearts

Article References: Worcester Polytechnic Institute researcher is seeking clues to problems in tiny hearts. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: fetal heart defects, coarctation of the aorta, digital twin, blood flow modeling, prenatal diagnosis, echocardiography, computational fluid dynamics, 3D printing, National Institutes of Health, Worcester Polytechnic Institute, congenital heart disease, biomedical engineering

The work, led by Sabah Noor with Nabeela Kousar, Khalil Ur Rehman and Wasfi Shatanawi, models blood as a so-called special third-grade fluid, a class of viscoelastic liquid whose stress response includes higher-order nonlinear terms. That choice matters. At low shear rates blood does not behave like water; its resistance to flow changes as it is continuously deformed by beating cilia and the sliding motion of an endoscope. Simpler non-Newtonian models such as Casson, Maxwell, Jeffrey or second-grade fluids can each capture one aspect of this behavior—yield stress, relaxation, or linear elasticity—but none account for the additional nonlinear elastic response that emerges under the complex, sustained deformation that characterizes cilia-driven endoscopic transport. The third-grade model, the authors argue, is the smallest framework that can represent these effects realistically.

The geometry of the problem is deliberately faithful to physiology. Two coaxial cylinders form the flow domain: the outer tube carries cilia on its inner surface, and these cilia beat asynchronously with a continuous phase lag between neighbors, producing a metachronal wave that travels along the wall. Depending on whether the wave and the effective stroke travel in the same or opposite directions, the beating is classified as symplectic or antiplectic—the former seen in the protozoan Opalina, the latter in Paramecium. Inside sits the endoscope, a solid rigid tube that moves axially at a fixed velocity, sweeping fluid along with it through the no-slip condition at its wall. Fluid occupies the gap between the two, bounded by constant-temperature walls that create a thermal gradient driving heat transfer.

On top of this mechanical picture, the researchers superimposed several physical effects that previous studies had treated only one at a time. An external radial magnetic field acts on the electrically conductive blood, generating Lorentz forces that oppose motion—the essence of magnetohydrodynamics, a field first described by Hannes Alfvén. The outer wall is treated as a porous medium, mimicking the permeability of biological tissue, which matters for predicting how fluid and suspended nanoparticles are absorbed into surrounding structures. Thermal radiation is included through the Roseland approximation, which is relevant for laser and thermal therapies where internal heat management is critical. And blood itself is transformed into a hybrid nanofluid by suspending two kinds of nanoparticles: zinc oxide (ZnO) and aluminum oxide (Al₂O₃).

The choice of nanoparticles is not arbitrary. ZnO offers chemical stability, low toxicity, antimicrobial activity, and proven biocompatibility, and it is already investigated for drug delivery, biosensing, and antiviral or anticancer applications. Al₂O₃ brings high thermal conductivity, corrosion resistance, and the ability to target specific tissues, improving treatment efficiency while limiting side effects. Combined at low volume fractions—no more than about three percent to avoid agglomeration and excessive viscosity—the two particles enhance heat transport while keeping the suspension stable enough for biomedical use. Blood’s ionic solution serves as the carrier fluid, with effective properties such as viscosity, density, thermal conductivity, and electrical conductivity computed through established hybrid-nanofluid mixing rules.

Perhaps the most significant departure from earlier work is the treatment of inertia. Most prior models of ciliary and peristaltic transport assumed creeping flow—negligible Reynolds number—which strips the governing equations of inertial terms. Here, the authors retained a moderate Reynolds number, between roughly 5 and 15, which is realistic for blood flow in larger vessels and keeps the momentum equations closer to their full form. Combined with the nonlinear shear-thickening rheology of the third-grade model, this produces a coupling among momentum transport, magnetic damping, porous drag, and heat transfer that simply cannot appear in creeping-flow formulations using conventional fluids. The cilia length parameter, wave number, and eccentricity of the elliptical ciliary stroke all enter directly through the boundary conditions at the outer wall, anchoring the mathematics to the actual beating motion of the biological structures.

Solving the resulting system of coupled nonlinear partial differential equations required a regular perturbation approach, carried out in two stages with the help of Mathematica. First, the equations were expanded in powers of the small wave number; then, because the axial momentum equation remained nonlinear even at zeroth order, a second perturbation was applied in the small third-grade parameter. The validity ranges—wave number and third-grade parameter both between 0.01 and 0.03—are small enough that neglected higher-order terms stay negligible. Residual analysis confirms convergence: maximum absolute errors were on the order of 10⁻⁶ to 10⁻⁸ for radial velocity, axial velocity, temperature, and pressure, indicating that the truncated series accurately approximates the true solution within its regime of validity.

The results reveal a rich interplay of competing mechanisms. Radial velocity falls as the radius ratio increases—the annular gap narrows, geometric confinement suppresses ciliary motion, and mass conservation forces the radial component to shrink—but rises dramatically with wave number and with cilia length, because longer cilia and shorter-wavelength metachronal waves transfer more momentum from wall to fluid. Doubling the wave number increased radial velocity by roughly 166 percent, and lengthening cilia by a modest fraction boosted it by nearly 87 percent. A faster-moving endoscope, by contrast, pushes fluid axially and weakens radial displacement.

Axial velocity behaves differently. It increases with radius ratio—momentum transfer from the moving endoscope intensifies in the confined space—and climbs steeply with wave number, roughly 200 percent over the studied range. Higher permeability of the porous wall reduces Darcy resistance and lets the fluid move more freely, raising axial speed by about a third, while a stronger magnetic field cuts axial velocity by roughly 30 percent as Lorentz forces impose electromagnetic drag. Notably, increasing the third-grade parameter raised axial velocity by about 60 percent: the nonlinear elastic stress terms let the fluid store deformation energy during ciliary pumping and endoscope motion and then release it back into the flow, facilitating axial momentum transport.

Temperature shows non-monotonic behavior in several cases. Increasing the third-grade parameter roughly doubles fluid temperature because enhanced axial motion strengthens convective heat transport from the hot wall. Permeability first raises temperature and then lowers it beyond a threshold, as convective retention of heat within the fluid gives way to radiative transfer toward the cooler wall. Magnetic field strength first cools the fluid by about 100 percent—Lorentz damping slows circulation—and then warms it again as heat accumulates in a stagnating fluid. Faster endoscope motion and higher Reynolds number both raise temperature by strengthening convection, while increasing the radiation parameter lowers it by distributing heat more uniformly.

Pressure responds as expected from the momentum balance. Stronger magnetic fields and larger third-grade parameters demand steeper pressure gradients to sustain flow—pressure rose 2.6 percent and 66 percent respectively across the tested ranges—while greater permeability and Reynolds number reduce the pressure needed. The team also examined bolus entrapment, the formation of recirculating fluid pockets trapped inside closed streamlines that travel with the metachronal wave. Bolus size grows with permeability and third-grade elasticity, because faster, more elastic fluid circulates more within each closed streamline, but shrinks under magnetic damping, which suppresses the overall velocity and traps less volume per pumping cycle.

The authors are candid about the model’s boundaries: velocity-slip and thermal-slip at the walls are neglected, the analysis is axisymmetric, and thermophysical properties are held constant. The perturbation solution is valid only for small wave numbers and weak third-grade effects, and stronger flows would require numerical methods. Even so, by uniting endoscope motion, magnetohydrodynamics, porous media, thermal radiation, ciliary propulsion, nonlinear blood rheology, and moderate inertia in a single analytically tractable framework, the study offers a physiologically grounded toolkit for designing magnetically controlled drug delivery, optimizing thermal therapies during endoscopy, and predicting how engineered nanoparticles will behave in the body’s ciliated passages. In an era when targeted nanomedicine is moving from bench to bedside, understanding these coupled transport physics is not an academic luxury—it is a prerequisite for safe and effective treatment.